While working with some people on their family tree, I've discovered that many of them keep their primary copy of their family tree on an online system. By this I mean that their original copy of their genealogical information is on a site like Ancestry.com or FamilySearch.org. I recommend against this.
While I trust Family Search to not go out of business and I know Ancestry performs backups of their data, I still would never put my trust into any one company outside of my control. I very much prefer to be in charge of my own data directly, then share it using any number of online services.
Given Ancestry's history of changing their mind on services they offer and information they will keep for their members, I hesitate to fully trust them. An example of this is Ancestry's yDNA and mtDNA services. They used to perform these tests, much like Family Tree DNA does, and make this data and your matches available to those who tested with them. With virtually no notice, Ancestry changed their mind and stopped offering the yDNA and mtDNA testing services. To make matters worse, they also deleted all of the data associated with these tests.
In addition, the investment company that owns the majority of Ancestry.com is exploring the sale of the company. While I'll never make alarming claims about what will happen after any sale, this is a good time to address the fact that we don't know what will happen after the sale and is a reminder that you should back up your data.
The way I look at it, the only person that you can count on to always have your best interests at heart is you. Store your data on your own home computer. In addition, always get a digital copy of all documentation to attach to your database. From there, you can upload your data to Ancestry, Family Search, RootsWeb or any other service you choose to use. This way, should the company you trust with your data ever have service or financial problems, the only thing in danger is the copy of the data you uploaded to them, and not your entire database, along with all the work you've put into it.
Now, don't take this as advice to have only one copy of your genealogical information and documentation in only one place, your own computer. You should always make sure you back up your data and never trust only one place to store it.
You can back it up any number of ways. Here are a few I recommend:
1. Use an online backup service. There are many to choose from. I make no claims as to any of the best and I don't necessarily endorse any of these. I only want to give you a place to start looking. http://www.backblaze.com, http://www.dropbox.com, http://www.google.com/drive, or http://www.mozy.com.
2. Use an external hard drive. I even recommend two external hard drives. The best part of using an external hard drive is that they're relatively inexpensive and you don't have an ongoing monthly charge for using them. Buying two is not expensive, even for a very large drives, and then you can bring one of them to an off-site location. This means that should disaster hit, and you lose your main computer and external hard drive in your home, you can retrieve your extra drive from the family member or even safety deposit box and keep any information you lost down to a minimum. Of course, this requires you to be vigilant and perform backups and switch the backup drives at your home and at your remote location on a regular basis.
3. Use BitTorrent Sync. You can find my writeup about this here: http://matthewkmiller.blogspot.com/2013/04/sharing-documentation-files-with.html . Bittorrent Sync allows you to share all of your data with anyone you wish to, automatically. Each of you would need to have BitTorrent Sync installed. You then share your private read-only or full edit key with the person you wish to share with. They will automatically download the files directly from your computer to theirs across the Internet. They can access the files and act as your backup.
If you don't already have all of your data stored locally on your home computer, I encourage you to download all of the data, along with a copy of all of the documentation now. You never know when an a company or organization will either change their mind about storing your data or becoming the victim of hackers or financial problems. Do this, and set up at least one of the backups listed above and rest peacefully knowing all your hard work is safe.